Given the context of the report, I still lean toward 3:30PM being the acknowledged end of the event, as in when Lavergne arrived at Ochsner. The medical records will show whether or not that's true. A stabbing (even a fake one) doesn't take half an hour, and it's highly unlikely even Lavergne would have claimed that he drove around aimlessly for hours after getting stabbed.
Lavergne would have been admitted, treated, and transferred to a private room before being interviewed by police, and it's safe to say that there would have been some wait between the time NOPD was called and the time they showed up in Jefferson Parish.